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Restricted choice?
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I declared this hand about a month ago and still have no idea what the correct play is, so I have come to Bridgewinners in search of enlightenment.

North
Q
J106
98
A1086543
South
AK742
Q4
K763
K7
W
N
E
S
P
P
1
1NT
P
3NT
P
P
P

Trick 1: 2-8-J-K

Trick 2: K-2-3-Q

Trick 3: 7-9-?

My immediate thought was to finesse, but before doing so I paused to see if I could work out any clues about the distribution. I came up with the following:

1. West has led 2. It can't be from a doubleton, and is extremely unlikely to be a singleton, as the trick 1 play marks West with T (also, West probably would have selected another lead with a singleton, and might have bid over 1NT with 9+ cards in the majors). It appears that West has 3+ diamonds, so East has at most 4.

2. If I take the bidding at face value, East appears to not have a 5-card major for his 4-card 1 opening. I therefore assumed that East has at most 4-4 in the majors.

3. From the play, East is known to have at most a doubleton club.

Putting these together, I concluded that East's shape had to be 3442, 4342, 4432, or 4441. Given that three of these four shapes include a doubleton club, I decided that even after taking restricted choice into account, East was a favourite to have QJ doubleton rather than Q singleton. (Even if East would only play Q from QJ from half the time, he was three times as likely to have started with QJ.) Accordingly, I played A at trick three - when East discarded, I was two down.

At the time, I felt that I had made the right play. I'm not so sure anymore, though - a few points that argue in favour of finessing:

1. In third seat, East might have chosen to open 1 with a poor five-card major on the side. This was the case on the actual hand - East had a 3541 shape with 98753.

2. If East is balanced, he would have opened 1NT with 15-17; thus, his range on the (344)2 hands is a bit narrower than his range on the 4441 hands, where he might have up to 15. This suggests that 4441 in East is a little more likely than might otherwise be the case.

In light of all this, I don't know whether it is right to finesse or play for the drop. It seems to me that to answer that question, I would need to weigh up the probabilities associated with these points 1 and 2, and I have no idea how to do that. I would be very interested to hear some thoughts about this hand.

Bonus question: what if East had opened in first seat, but the auction was otherwise the same?

Bonus question 2: would you bid 1 or 1NT with my hand?

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